Timeline for Definition of Cartan Model - Equivariant differential forms
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2023 at 1:30 | comment | added | Dmitri Pavlov | For ΩM, this is just the Lie derivative of differential forms. You can find the definition in any book on differential geometry, see, for example, Section 7.5 in Lee's Manifolds and Differential Geometry. Sg* is a (degreewise) finite-dimensional space, so you can differentiate normally. | |
| Apr 27, 2023 at 21:12 | comment | added | Nash-iOS | I think I need more information. What kind of sections are $S(g^*)$? Also, could you provide more information (or references) on how to differentiate sections? | |
| Apr 27, 2023 at 14:47 | comment | added | Dmitri Pavlov | Given an element x in the Lie algebra of G, act by the element exp(tx) on the vector space Sg*⊗ΩM (its elements are smooth sections of a vector bundle), then differentiate with respect to t. Sections of vector bundles are differentiated pointwise. | |
| Apr 27, 2023 at 7:05 | comment | added | Nash-iOS | @DmitriPavlov, $G$ acts on tensor product $ S(g^*) \otimes \Omega(M)$ which is not a manifold. What do you mean by differentiating the action? | |
| Apr 27, 2023 at 0:07 | comment | added | Dmitri Pavlov | To pass from 2 to 1, simply differentiate the action of G, obtaining an action of the Lie algebra of G. | |
| S Apr 26, 2023 at 20:44 | review | First questions | |||
| Apr 26, 2023 at 23:02 | |||||
| S Apr 26, 2023 at 20:44 | history | asked | Nash-iOS | CC BY-SA 4.0 |